We search for decays of a B meson into a neutral D meson and a charged kaon, with the D meson decaying into a charged kaon, a charged pion, and a neutral pion. This final state can be reached through the b→c transition B-→D0K- followed by the doubly Cabibbo-suppressed D0→K+π-π0, or the b→u transition B-→D̄0K- followed by the Cabibbo-favored D̄0→K+π-π0. The interference of these two amplitudes is sensitive to the angle γ of the unitarity triangle. We present results based on 226×106 e+e-→Υ(4S)→BB̄ events collected with the BABAR detector at SLAC. We find no significant evidence for these decays and we set a limit RADS≡Γ([K+π-π0]DK-)+Γ([K-π+π0]DK+) Γ([K+π-π0]DK+)+Γ([K-π+π0]DK-)<0.039 at 95% confidence level, which we translate with a Bayesian approach into rB≡|A(B- →D̄0K-)/A(B-→D0K-)|<0.19 at 95% confidence level. © 2007 The American Physical Society.